J. Japan Statist. Soc., Vol. 33 (No. 1), pp. 119-136, 2003

Effect of W, LR, and LM Tests on the Performance of Preliminary Test Ridge Regression Estimators

B. M. Golam Kibria and A. K. Md. E. Saleh

Abstract. The preliminary test ridge regression estimators (PTRRE) based on the Wald (W), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests are considered in this paper. Using risks, the regions of optimality of the estimators are determined. Under the null hypothesis, the PTRRE based on LM test has the smallest risk followed by the estimators based on LR and W tests. However, the PTRRE based on W test performs the best followed by the LR and LM based estimators when the parameter moves away from the subspace of the restrictions. The conditions of superiority of the proposed estimator for both shrinkage parameter and departure parameter are given. Some tables for maximum and minimum guaranteed relative efficiency of the proposed estimators have been provided. These tables allow us to determine the optimum level of significance corresponding to the optimum estimators among proposed estimators. Finally, we conclude that the optimum choice of the level of significance becomes the traditional choice by using the W test for all non-negative shrinkage parameter.

Key words and phrases: Lagrangian multiplier, likelihood ratio test, preliminary test, ridge regression, risk, superiority, Wald test.

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